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In my last blog post I updated my definition for a fact. The definitions of three other terms were improved per feedback received. To provide a bit of context, these terms relate to the notion of creating a verifiably true and fair representation of financial information within the Guide to Verification of an SEC XBRL Financial Report, but apply to other documentation as well.

As stated within the Guide to Verification of an SEC XBRL Financial Report, a financial report can be said to be valid if it possesses certain traits which can be defined in general terms and for clarity are listed below to bring them into the reader's mind:

Completeness: Having all necessary or normal parts, components, elements, or steps; entire.

Consistency: Compatible or in agreement with itself or with some group; coherent, uniform, steady. Holding true in a group, compatible, not contradictory.

Accuracy: Correctness in all details; conformity or correspondence to fact or given quality, condition; precise, exact; deviating only slightly or within acceptable limits from a standard.

While these four notions which relate to the "trueness" and "fairness" must exist for every fact reported by a financial report, they also need to exist when considering the financial report in its entirety.

Two other notions help bring the notion of trueness and fairness of information at the fact and at the report level into focus. These are the improved definitions of these two terms:

Fidelity: Fidelity relates to the loyal adherence to fact or detail; exactness. The representation of the facts and circumstances represented within a financial report properly reflect, without distortion, reality. High fidelity is when the reproduction (a financial report) with little distortion, provides a result very similar to the original (reality of company and environment in which company operates).

Integrity: Integrity is holistic fidelity. Integrity relates to the fidelity of the report in its entirety, of all parts of a financial report, from all points of view. Integrity is holistic accuracy, accurate as a whole. Integrity is the quality or condition of being whole or undivided; completeness, entireness, unbroken state, uncorrupt. Integrity means that not only is each component of a financial report is correct but all the pieces of the financial report fit together correctly, all things considered.

In much of my documentation I also used integrity to mean something else. I have untangled this terminology and introduced another term, intersection.

To understand integrity correctly, it is important to understand the notion of an "intersection". An intersection is defined as:

Intersection: An intersection is a physical connection between two pieces of a financial report. Generally an intersection is some report element such as a [Table], an [Axis], a [Member] or a Concept. Intersections can be further explained by business rules.

An example will help you understand the notion of an intersection. Consider the concept "inventories". Inventories might appear as a line item on the balance sheet. Total inventories might be detailed or a breakdown provided within the disclosures. While the label "Inventories" might appear on the balance sheet and perhaps "Total inventories" in the disclosures, that is actually on reported fact presented in two places within a financial report. That fact has the characteristic of both relating to the same concept. All other characteristics are likewise the same. In essence the fact intersects the balance sheet with the detailed breakdown of inventories, it defines an intersection.

Looking at this from another perspective helps see the importance of intersections. What if this information was modled incorrectly and rather being expressed as one single fact shared by to components of a financial report; and rather two different concepts were used and two different facts provided within a financial report. In this case, the intersection between the two components would be masked. As a result, errors could be introduced within the financial report and the error would likewise be masked. For example, if two facts are modeled and the balance sheet fact was one number and the detailed breakdown of total inventories was some different number then the balance sheet and the detailed breakdown would not agree.

Part of integrity is that there are no such modeling mistakes and therefore no mathematical errors which could possibly be masked by a modeling mistake.

Some software leverages these sorts of intersections, other software does not. I pointed out some time ago that intersections were leveraged within the Firefox add-on for XBRL. At that time I used the term hypercube jumping to describe this. The XBRL Cloud Viewer leverages these sorts of intersections. CoreFilings Magnify does. Other software likely does also.

The mistake I made with the term integrity was that I was using it to mean both the definition of integrity above and the notion of an intersection. The improvement is that I recognize that these are two different notions so they need to different terms, even though the two notions are related to a degree.